   Chapter 8.4, Problem 49E

Chapter
Section
Textbook Problem

True or False? In Exercises 47-50, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If x = tan θ , then ∫ 0 3 d x ( 1 + x 2 ) 3 / 2 = ∫ 0 4 π / 3 cos θ   d θ

To determine
Whether the statement “If x=tanθ, then 03dx(1+x2)32=04π3cosθdθ” is true or false.

Explanation

The statement is;

If x=tanθ, then 03dx(1+x2)32=04π3cosθdθ.

Put x=tanθ in the integration 03dx(1+x2)32.

The derivative of x=tanθ with respect to θ is;

dx=sec2θdθ

Now, when x=0 the value of θ is;

0=tanθθ=0

Now, when x=3 the value of θ is;

3=tanθθ=π3

So, the integration 03dx(1+x2)32 can be expressed as;

03

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Expand each expression in Exercises 122. (2x3)2

Finite Mathematics and Applied Calculus (MindTap Course List)

In problems 63-73, factor each expression completely. 66.

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the integral, if it exists. 04x1dx

Single Variable Calculus: Early Transcendentals

The polar coordinates of the point P in the figure at the right are:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The area of the region at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th

Why are studies that examine the effects of aging not considered true experiments?

Research Methods for the Behavioral Sciences (MindTap Course List) 